12/16 simplified

Simplifying 12/16: A Step-by-Step Solution

Introduction

In this article, we will explore the process of simplifying the fraction 12/16. We will explain what this question means and provide a step-by-step solution to find the simplified form of the fraction. Additionally, we will discuss the concept of finding the Greatest Common Divisor (GCD) or Highest Common Factor (HCF) and provide examples related to simplifying fractions.

What does this question mean?

The question "What is the answer to 12/16 simplified?" is asking us to find the simplest form of the fraction 12/16. Simplifying a fraction involves reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common divisor.

Answer: 12/16 simplified

Before diving into the method, let's find the answer to the question. The simplified form of 12/16 is 3/4.

Method: Tips

To simplify a fraction, follow these steps:

1. Find the GCD (or HCF) of the numerator and denominator.
2. Divide both the numerator and denominator by the GCD.
3. The resulting fraction is the simplified form.

Step-by-Step Solution

Now, let's go through the step-by-step solution to simplify 12/16:

Step 1: Find the GCD of 12 and 16.

• The factors of 12 are 1, 2, 3, 4, 6, and 12.
• The factors of 16 are 1, 2, 4, 8, and 16.
• The common factors of 12 and 16 are 1, 2, and 4.
• The GCD of 12 and 16 is 4.

Step 2: Divide both the numerator and denominator by the GCD.

• Divide 12 by 4: 12/4 = 3.
• Divide 16 by 4: 16/4 = 4.

Step 3: The resulting fraction is 3/4, which is the simplified form of 12/16.

Solved Examples Related to 12/16 Simplified

Let's explore a few examples to further understand the concept of simplifying fractions:

Example 1: Simplify 18/24.

• Find the GCD of 18 and 24: GCD(18, 24) = 6.
• Divide 18 by 6: 18/6 = 3.
• Divide 24 by 6: 24/6 = 4.
• The simplified form of 18/24 is 3/4.

Example 2: Simplify 9/15.

• Find the GCD of 9 and 15: GCD(9, 15) = 3.
• Divide 9 by 3: 9/3 = 3.
• Divide 15 by 3: 15/3 = 5.
• The simplified form of 9/15 is 3/5.

How to Find GCD (or HCF)?

To find the GCD (or HCF) of two numbers, follow these steps:

1. List all the factors of both numbers.
2. Identify the common factors.
3. The largest common factor is the GCD (or HCF).

For example, to find the GCD of 12 and 16:

• The factors of 12 are 1, 2, 3, 4, 6, and 12.
• The factors of 16 are 1, 2, 4, 8, and 16.
• The common factors of 12 and 16 are 1, 2, and 4.
• The GCD of 12 and 16 is 4.

Conclusion

Simplifying fractions involves finding the simplest form by dividing both the numerator and denominator by their greatest common divisor. In the case of 12/16, the simplified form is 3/4. By following the step-by-step solution and understanding the concept of finding the GCD, we can easily simplify fractions and express them in their lowest terms.